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If A and B are matrices with 24 and 40 elements respectively, then the number of possible orders of A and B such that A B is defined is

Options

  1. A2
  2. B3
  3. C4
  4. D8

Correct answer

C. 4

Step-by-step solution

If A B is defined then order of A must be m × n and order of B is n × p m n = 24 = 2 3 × 3 n p = 40 = 2 3 × 5 n can be 2 0 , 2 1 , 2 2 , 2 3 There are only 4 possibilities of n , so the number of possible orders of A , B is 4

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